Year: 2026
Type: preprint
Abstract: Baxter's classical theorem for orthogonal polynomials on the unit circle establishes that the linear Fourier coefficients of a measure are in $\ell^1$ if and only if the nonlinear coefficients, i.e., the so-called Verblunsky coefficients, are in $\ell^1$. However, this equivalence is purely qualitative. We explore possible formulations of such quantitative theorems with norm and Lipschitz estimates for the $SU(2)$-valued nonlinear Fourier transform, for which the analog of Baxter's theorem has been recently obtained. In particular, the highlight of this paper is a number-theoretic construction for the NLFT which proves some negative results in this direction. We also prove a positive result and discuss the limitations of Baxter's method.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G6444257319, G7301595098
OpenAlex ID: W7216376403